A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

Ion conductive characteristics of cross-linked network polysiloxane-based solid polymer electrolytes

A series of cross-linked network polysiloxanes containing oligoethylene oxide units, (OCH₂CH₂)_n, as internal free chains have been synthesized by performing hydrosilylation of partially PEO-substituted polysiloxane precursor with , ω-diallyl terminated poly(ethylene glycol). The polymer electrolytes were formed by complexing with LiN(CF₃SO₂)₂ electrolyte salt and exhibited superior conductive property. The σ_RT of the network polymer electrolytes is in the range of 2.50×10⁻⁵ to 1.62×10⁻⁴ S/cm and depends on the cross-linking density (in terms of Si–H amount of the siloxane precursor), repeating unit number of internal oligoethylene oxide and chain length of the cross-linker. The significant enhancement of the conductivity was observed when low molecular weight dimethyl poly(ethylene glycol) was added as plasticizer. The temperature dependence of the ionic conductivity was also studied, following the Vogel–Tamman–Fulcher (VTF) equation.     

Sur un théorème de métrisabilité

Sans résumé     

Harmonic conformal flows on manifolds of constant curvature

We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.      

The numerical index of the space

We give a partial answer to the problem of computing the numerical index of for .

     

Annealed Lower Tails for the Energy of a Charged Polymer

We consider a randomly charged polymer. Each monomer carries a random charge, and only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.     

The Lie theory of certain modular form and arithmetic identities

Modular form identities lying in the framework of Shimura’s theory of nearly holomorphic modular forms are obtained by Lie theoretic means as consequences of identities relating the Maass–Shimura operator and the Rankin–Cohen brackets, which in turn follow from change-of-basis formulae in the theory of Verma modules. The Lie theoretic origin of known van der Pol and Lahiri-type arithmetic identities is thus unveiled, and similar new ones are derived in a systematic way. These identities relate divisor functions, Ramanujan’s τ-function and functions defined by the Fourier coefficients of other cusp forms and involve hybrid coefficients, drawn from Lie theory and number theory, given explicitly by formulae combining the arithmetic Clebsch–Gordan coefficients and the Bernoulli numbers. A few side results, interesting in their own right, such as Leibniz-type rules satisfied by the Rankin–Cohen brackets, are also obtained.     

Suppressing Universal Cathode Crossover in High-Energy Lithium Metal Batteries via a Versatile Interlayer Design**

The universal cathode crossover such as chemical and oxygen has been significantly overlooked in lithium metal batteries using high-energy cathodes which leads to severe capacity degradation and raises serious safety concerns. Herein, a versatile and thin (≈25 μm) interlayer composed of multifunctional active sites was developed to simultaneously regulate the Li deposition process and suppress the cathode crossover. The as-induced dual-gradient solid-electrolyte interphase combined with abundant lithiophilic sites enable stable Li stripping/plating process even under high current density of 10 mA cm⁻². Moreover, X-ray photoelectron spectroscopy and synchrotron X-ray experiments revealed that N-rich framework and CoZn dual active sites can effectively mitigate the undesired cathode crossover, hence significantly minimizing Li corrosion. Therefore, assembled lithium metal cells using various high-energy cathode materials including LiNi_0.7Mn_0.2Co_0.1O₂, Li_1.2Co_0.1Mn_0.55Ni_0.15O₂, and sulfur demonstrate significantly improved cycling stability with high cathode loading.     

Positive Elements and Automatic Continuity of Algebra Morphisms

We use positive elements of Hermitian algebras to give results on automatic continuity of algebra morphisms. Consequences and applications are also given.